1cm = 10-1 meter (m)1 km = 103 m

100 km = 105 m1000 km = 106 mlight year = 1016 m

1 mm = 10-3 m

1 micrometer = 1 µm = 10-6 m

1 nanometer = 1 nm = 10-9 m

https://www.youtube.com/watch?v=Usj6viU0AaI

1cm = 10-1 meter (m)1 km = 103 m

100 km = 105 m1000 km = 106 mlight year = 1016 m

1 mm = 10-3 m

1 micrometer = 1 µm = 10-6 m

1 nanometer = 1 nm = 10-9 m

https://www.youtube.com/watch?v=Usj6viU0AaI

Today’s Plan• A few class logistics

• Scientific Notation

• Units and Converting Units

• Estimation

• Significant Figures

• Brief trigonometry review(?)

• NOT polar coordinates or atoms/quarks (Sec. 1.2)

Extra Practice Problems (Answers in back of book): 1.7, 1.9, 1.11, 1.15, 1.19, 1.21, 1.23, 1.31, Conceptual 1, 5, & 11

Overview of notecard answers

• Improve critical thinking/analysis

• Like physics and/or “required class”

• Learn physics ☺ ︎

• Some of you are completely new, some have had physics before.

Homework and Reading Assignments

Due day before next class, midnight(today’s: due tomorrow, 11:59pm)

Note: extra credit for correct answers, 11am before class.

Homework and Reading Assignments

Due day before next class, midnight(today’s: due tomorrow, 11:59pm)

Note: extra credit for correct answers, 11am before class.

Homework and Reading Assignments

Due day before next class, midnight(today’s: due tomorrow, 11:59pm)

Note: extra credit for correct answers, 11am before class.

Homework and Reading Assignments

Due day before next class, midnight(today’s: due tomorrow, 11:59pm)

Note: extra credit for correct answers, 11am before class.

iClickers

• Starting next Wednesday

• 20% correctness, 80% participation

• iClicker Registration :

• When you register on eCampus, it will show you which number is needed off of the back of the iClicker.

Yippee!

Questions? Need help?

Contact iclicker at support@iclicker.com or by phone at 866-209-5698.

• Scientific Notation

• Units and Converting Units

• Estimation

• Significant Figures

• Brief trigonometry review?

• NOT polar coordinates or atoms/quarks (Sec. 1.2)

Main ideas today

Extra Practice Problems (Answers in back of book): 1.7, 1.9, 1.11, 1.15, 1.19, 1.21, 1.23, 1.31, Conceptual 1, 5, & 11

Scientific notation

6.022 x 103 inches

6,022 inchesis the same as saying6.022 x 1000 inches

is the same as

Scientific notation

6.022 x 103 inches

6,022 inchesis the same as saying6.022 x 1000 inches

is the same ascoefficient

Only one digit between 1-9 on left of decimal!

Scientific notation

6.022 x 103 inches

6,022 inchesis the same as saying6.022 x 1000 inches

is the same as

base

coefficient

Only one digit between 1-9 on left of decimal!

Scientific notation

6.022 x 103 inches

6,022 inchesis the same as saying6.022 x 1000 inches

is the same as

base

coefficient

Only one digit between 1-9 on left of decimal!

exponent (“order of magnitude”)

Direction and number of spots the decimal point

is shifted

Scientific notation

• Warnings:

• To write in WebAssign or Google, you would write “3.72e+23” (or with all the zeros)

• For example, “0.000023” and “2.3e-5” are same in WebAssign

• EE in calculator, not ex

~37,200,000,000,000cells in body

~200,000,000,000galaxies (in known universe)

3.72 x 1013 cells 2 x 1011 galaxies3.72 x 1013 cells 2 x 1011 galaxies

LONG NUMBER SHORT-HAND

Take a relaxing drive to Canada

Take a relaxing drive to Canada

UnitsIn the fateful year 1960…

“Nah”“UNITE!”(Metric/SI system) (Imperial system)

meter = 3.28 ftkilogram = 2.2 lb

second

foot = 0.30 mpound = 0.45 kg

second

Approximate Values in SI UnitsHeight of person

~ 2 m (6.5 feet)

Average weight of person

~ 80 kg (176 lbs.)

Would 100 kg be an incorrect estimate?

Average life of person

~ 2 x 109 s (2 billion seconds) = 63.4 years

UnitsSome common short-hands for scientific notation

Units

Scientific Notation: 2 x 10-9 m Big or Small?

Some common short-hands for scientific notation

Units

Prefixes: kilo(k) = 103 or 1000

centi(c) = 10-2 or 1/100 milli(m) = 10-3 micro(µ) = 10-6 nano(n) = 10-9

Scientific Notation: 2 x 10-9 m Big or Small?

Some common short-hands for scientific notation

Units

Conversion examples: 1 kilometer (1km) = 1000 meters (1000 m)

1000 mm = 1m 1000 grams = 1 kg

Prefixes: kilo(k) = 103 or 1000

centi(c) = 10-2 or 1/100 milli(m) = 10-3 micro(µ) = 10-6 nano(n) = 10-9

Scientific Notation: 2 x 10-9 m Big or Small?

Some common short-hands for scientific notation

101.2

ALWAYS use

units!

Units and Dimensional AnalysisI won’t test you on this explicitly, but it makes

everything easier.

A + B = CTo add terms together, they must have the same units.

7 m + 10 m = 17 m

A x B = CUnits on each side of the equation must be the same.

Speed x time = distance travelled60 x 2 h = 120 kmkm

h

Conversion of units• You might need to convert from familiar to

standard units or vice versa

Conversion of units• You might need to convert from familiar to

standard units or vice versaA student is going to study abroad during the summer and is looking for an apartment in Europe. She finds an ad for an apartment of 90 square meters. How many square feet is that? Is this a big apartment? (1 m = 3.28 ft)

Conversion of units• You might need to convert from familiar to

standard units or vice versaA student is going to study abroad during the summer and is looking for an apartment in Europe. She finds an ad for an apartment of 90 square meters. How many square feet is that? Is this a big apartment? (1 m = 3.28 ft)

90 m2

Conversion of units• You might need to convert from familiar to

standard units or vice versaA student is going to study abroad during the summer and is looking for an apartment in Europe. She finds an ad for an apartment of 90 square meters. How many square feet is that? Is this a big apartment? (1 m = 3.28 ft)

90 m2 3.28 ft 1 mX

Conversion of units• You might need to convert from familiar to

standard units or vice versaA student is going to study abroad during the summer and is looking for an apartment in Europe. She finds an ad for an apartment of 90 square meters. How many square feet is that? Is this a big apartment? (1 m = 3.28 ft)

90 m2 3.28 ft 1 mX

3.28 ft 1 mX

Conversion of units• You might need to convert from familiar to

standard units or vice versaA student is going to study abroad during the summer and is looking for an apartment in Europe. She finds an ad for an apartment of 90 square meters. How many square feet is that? Is this a big apartment? (1 m = 3.28 ft)

90 m2 3.28 ft 1 mX = 968 ft23.28 ft

1 mX

Fast or slow?1 mile = 1.6 x 103 meters

HOW MANY MILES PER HOUR?

“Order of magnitude” Estimation

“Order of magnitude” Estimation

• Sometimes an exact answer is not necessary. Within a factor of 10 might be fine.

“Order of magnitude” Estimation

• Sometimes an exact answer is not necessary. Within a factor of 10 might be fine.

• Used when you only need to “estimate”

“Order of magnitude” Estimation

• Sometimes an exact answer is not necessary. Within a factor of 10 might be fine.

• Used when you only need to “estimate”

• Cost to buy carpet for a room.

“Order of magnitude” Estimation

• Sometimes an exact answer is not necessary. Within a factor of 10 might be fine.

• Used when you only need to “estimate”

• Cost to buy carpet for a room.

• Time to pay off student loans, a car, etc.

“Order of magnitude” Estimation

• Sometimes an exact answer is not necessary. Within a factor of 10 might be fine.

• Used when you only need to “estimate”

• Cost to buy carpet for a room.

• Time to pay off student loans, a car, etc.

• How many gumballs fit in a jar (contests).

“Order of magnitude” Estimation

• Sometimes an exact answer is not necessary. Within a factor of 10 might be fine.

• Used when you only need to “estimate”

• Cost to buy carpet for a room.

• Time to pay off student loans, a car, etc.

• How many gumballs fit in a jar (contests).

• Use whenever uncertainty in numbers is large.

Significant Figures• Measurements are not typically perfect

• Even if not estimating, there is some error

• Significant figures are used to indicate how confident you are in the number given

22 inches means accurate to 1 inch (means it could be 21 to 23 inches)

2 significant figures

22.0 inches means accurate to 0.1 inches (or 21.9 to 22.1 inches)

3 significant figures

Significant Figures• Measurements are not typically perfect

• Even if not estimating, there is some error

• Significant figures are used to indicate how confident you are in the number given

22 inches means accurate to 1 inch (means it could be 21 to 23 inches)

2 significant figures

22.0 inches means accurate to 0.1 inches (or 21.9 to 22.1 inches)

3 significant figures

“97.7 +/- 2”

Significant Figures in Scientific Notation

• All Significant Figures should always appear when a number is in scientific notation.

• Examples:

1204.730 1.204730 x 103Scientific notation

Significant Figures in Scientific Notation

• All Significant Figures should always appear when a number is in scientific notation.

• Examples:

1204.730 1.204730 x 103

How many significant figures are in this number?

1200….. is it 1.2 x 103 OR 1.20 x 103 OR 1.200 x 103 ?

If needed, problem should state uncertainty

Scientific notation

Significant Figures • Sum or subtraction: use accuracy of least accurate

number (decimal position) - 120.031 + 11.3 = 131.3

• Multiplication or division: use smallest number of significant digits.- 28.0 × 21.3 = 596- 28 × 21.3 = 600 or 6.0 × 102

• My tests and WebAssign will not explicitly test you on significant figures (3 or 4 will be fine).

• If use less, WA might give you an error.

Remember• ALWAYS USE UNITS!

• Dimensional analysis

• Treat units like a variable!

• Both sides must match!

• Estimation

• OK when data not precise.

• Significant figures

• May save your life some day

Practice Conversions and Sig Figs

• A rectangular building lot measures 104 ft by 151 ft. Determine the area of this lot in square meters (m2). Area = length x width

(1 m = 3.28 ft)

Practice Conversions and Sig Figs

• A rectangular building lot measures 104 ft by 151 ft. Determine the area of this lot in square meters (m2). Area = length x width

• Two possible strategies. Convert ft to meters of each dimension before multiplying OR

(1 m = 3.28 ft)

Practice Conversions and Sig Figs

• A rectangular building lot measures 104 ft by 151 ft. Determine the area of this lot in square meters (m2). Area = length x width

• Two possible strategies. Convert ft to meters of each dimension before multiplying OR

• Find the answer in square feet and then convert to square meters

(1 m = 3.28 ft)

Practice Estimation: The Importance of Recycling

Soft drinks are commonly sold in aluminum containers. Estimate how many such containers are thrown away or recycled each year by U.S. consumers?

Practice Estimation: The Importance of Recycling

Soft drinks are commonly sold in aluminum containers. Estimate how many such containers are thrown away or recycled each year by U.S. consumers?

In some states, you can get 5 cents per can. Estimate how much money would you get if you recycled all of the cans in the US for one year?

Practice Estimation: The Importance of Recycling

Soft drinks are commonly sold in aluminum containers. Estimate how many such containers are thrown away or recycled each year by U.S. consumers?

In some states, you can get 5 cents per can. Estimate how much money would you get if you recycled all of the cans in the US for one year?About how much would the average US citizen get?

SOH CAH TOA!

SOH CAH TOA!For right triangles…

θopp

adj

hyp

SOH CAH TOA!For right triangles…

adjacentoppositetan

hypotenuseadjacentcos

hypotenuseoppositesin

=

=

=

θ

θ

θ

θopp

adj

hyp

SOH CAH TOA!For right triangles…

adjacentoppositetan

hypotenuseadjacentcos

hypotenuseoppositesin

=

=

=

θ

θ

θ

θopp

adj

hyp

222 cba =+(Pythagorean Thm.)

c = hypotenuse

Example: Surveying the River

A surveyor wants to measure the distance across a river. Starting directly across from a tree on the opposite bank, he walks 100 m along the

riverbank to establish a baseline. Then, he sights across to a big tree. The angle from his baseline to the tree is 35 degrees. How wide is the river?

Draw a picture.

river

Example: Surveying the River

A surveyor wants to measure the distance across a river. Starting directly across from a tree on the opposite bank, he walks 100 m along the

riverbank to establish a baseline. Then, he sights across to a big tree. The angle from his baseline to the tree is 35 degrees. How wide is the river?

Draw a picture.

100 m

river

People often struggle with large number math.

Powerball “Math”

People often struggle with large number math.

Powerball “Math”

1.3x109

3.0x108